Numbers ending in 2, 3, and 4 (Excluding 12/13/14) take the genitive singular.
It is the myriads of exclusions that I find frustrating at the moment... Nevermind, I will hopefully "get there" eventually with patience...
I wouldn't really consider 12, 13, and 14 to be exclusions since, as the "Tips and notes" (https://www.duolingo.com/skill/ru/Time-and-Numbers) point out, they are numbers larger than four and therefore take the genitive plural.
Yeah, but 22 follows the 2 and 23 follows the three etc. so are 42, 53, 64 etc.., right? But 12, 13 and 14 follows the 'larger than four' rule...
Look at how they are formed in Russian:
- 22 is два́дцать две́ [feminine] or два́дцать два [masculine or neuter] (therefore, it uses the noun form for две/два),
- 23 is два́дцать три (therefore, it uses the noun form for три),
- 42 is два́дцать два/две,
- 53 is пятьдеся́т три,
- 64 is шестьдеся́т четы́ре.
At the same time, numbers from 11 to 19 are formed differently (the pattern was like 'one-on-ten', 'two-on-ten'):
- двена́дцать ends in -дцать, which is a contracted form of десять and therefore you use the noun form for десять,
- трина́дцать ends in -дцать,
- четы́рнадцать ends in -дцать.
The way these numbers are formed is really an exception (for ten, you use 'one-on-ten' pattern; for other tens, you use 'twenty one' pattern), but the noun form choice doesn't seem too illogical to me.
Because it follows the hard consonant (and is not separated by a pause). «И» cannot be pronounced after a hard consonant, so when it follows a hard consonant, it becomes ы.
When you add a prefix to a word beginning with И, it becomes Ы: без 'without' + изве́стный 'famous' = безызве́стный 'obscure'.
However, when it's written as a separate word, we don't change the spelling. However, if separate words are pronounced without a pause, we still pronounce [ы]: без 'without' + изве́стий 'news' = без [ы]зве́стий 'without news'.